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Imagine stumbling through a friendly family corn maze, dizzily spinnng, careening off the vegetation walls. The sky has long since turn from blue to orange and is now a darkening gray. Corn shadows lengthened as you bravely searched, until the stalks became simple, evil, black silhouettes cut from the heavens. Every junction looks like every other. Did you turn left last time you were here? Right? You hear the panicked breathing of your spouse. Both of you have the same thing in mind, but neither will mention it: Should you eat the spouse or the children first if it came to that? You shake the thoughts from your head. Then you realize it: Your cell phone. You dial 911 and within minutes you hear sirens and bloodhounds. You are rescued. Never again, you swear, will you try a corn maze.

So that you don't have to suffer injury or embarassment, I'm going to teach you how to escape from any maze. It is a simple trick. So simple that you don't need a map or even vision. You could do it blindfolded. Here it is:

TOUCH THE WALL WITH ONE HAND AND WALK FORWARD.

That is literally it. Stick out your right hand and keep it on the wall as you walk and eventually you will reach the exit. It is guaranteed. The unfortunate family that was lost at Connors Farm was apparently in the horse's nose. You can see from the map that they were very close to the exit by the shortest route, but let's suppose they were pointed the other way. Armed with the right hand rule they would have followed the red path below. Try it with an equivalent left hand rule, you'll see that the family still escapes by a different route. Going south with the left or right hand rule leads to the exit very quickly.

I was prompted to write this because literally the next thing I read on the Internet, after reading about this lost family, was someone commenting that school was a waste of time since there is no use for higher math. I had to laugh, because it is exactly a slightly higher mathematical understanding that leads to knowing how easy it is to escape mazes. The one hand technique works because a maze is just like a string.

Imagine a long string on the ground. You can follow that string from start to finish by holding it with one hand and walking. If that string were looped around in a circle so that the beginning and end were close to each other it still wouldn't matter, you could walk the string from beginning to end. What if you poked in bits of the string? Doesn't change it, it's a string and can still be walked. What if you poked in the string and distorted it into really complicated shapes? Still you could walk it. That's exactly what a maze is and that's why you can get out by following a wall.

Now, there is an exception. You have to be lucky enough to touch an outside wall, but the good news is that most mazes are composed exclusively of walls connected to the outside. If the maze has disconnected islands then you have a problem using this trick becauses you would circle the island you had your hand on. In the string analogy, this is like a second loop of string inside the larger loop of string. If you grab hold of the second string then you will forever walk around that one, never moving to the larger string.

At Connors farm such islands do exist in many places. The hooves and legs, for example, contain many of these islands. You have to use a slightly more complicated algorithm to get out of a maze that has islands in it.

You must think of a way to leave messages for yourself on the ground, like breaking off a corn stalk and laying it down. This is because you need to keep track of where you've been and which paths turn out to be dead ends. Such a system might work thusly:

At the junctions lay down a stalk along the path you came from and along the path you left by.

If you hit a dead end, go back to the last junction and close off the path by turning the stalk 90 degrees (see step 3-4 below).

Now if you ever go to that junction again, you can quickly see which paths are dead ends for sure and which you've never visited

empty paths are unvisited

in-line stalks mean the path you are currently trying but might have to backtrack

blocked paths are proven dead ends.

Then pick a new path, or of none exist then continue backtracking by paths that you haven't blocked yet. Remember to block paths behind you as you backtrack by turning the stalk 90 degrees.

It is also a dead end if you return to a junction you've already visited even if it's by a different path.

Just mark that path with a 90 degree stallk and turn around (step 4).

Eventually you will reach the exit.

The path you took (without the dead ends) are marked by stalks that are in line (step 6)

There you have some examples of how a little higher education, at least a little lesson in logic, could save you from an embarassing 15 minutes of fame.

What's your take? Are you going to teach your children these lifesaving techniques? Do you think higher logic and math is useful in "REAL" life?

Hope you liked the post. Please do me a favour ...

Comments

What a great application of higher math! I wrote a post once about why it's useful to know higher math, but this is a real life application... Being a math teacher, I love math, and I see math everywhere, but I know a lot of people hated math in school and see no point in it. If they don't like math, they will obviously try to find every way of discounting its worth. But let's face it, without math there would be no advancement in technology. There would be no computers, no TV's, no smart phones. All the technology (new and old) is based on math principles. Just because there is something more difficult than we can understand doesn't mean it's actually not useful. Thanks for this wonderful and simple application of higher math. BTW, I always wanted to do a corn maze like that... now that I know how to get out if I get stuck, I'll have to get into one with my kids before Hallowe'en.

I agree with you. I think mainly the people who say they don't use math don't use it because they don't like it. I find ways of using most of the stuff I know, just because I know it. If I didn't know it I wouldn't use it, and probably wouldn't realize that it was useful. Some of the things I'm talking about are just realizing how things work. For example, people often have financial advice, but that financial advice just seems so basic because I know it. In fact, most of it seems a little wrong because it is pretty obvious that the person giving it doesn't actually know it ... they just repeat something they heard elsewhere and know it superficially. I'm not saying I know everything to the bottom, but when you know more that someone else then you can detect some of their lacking areas. Same with parenting. A lot of people give parenting advice that just sounds "nice", but has little basis in the science of behaviour and psychology, or they misapply some tidbit they heard somewhere. Again, I'm just an amateur psychologist, but I integrate things pretty well and I also experiment on myself and others to a large degree, including my dogs, which are among the best behaved and most intelligent dogs you'll see outside of performance dogs. If they don't work then I don't repeat 'em. Anyway, the more you know the more you can understand about the world.

I love your approach. But there seems another way to figure this out... Choose a direction, any direction, and WALK THROUGH THE EVER-LOVIN CORN for crying out loud! Forgive me because I'm a city boy, but it's CORN right? We're not talking real walls here.

As a father myself, if I had truly felt that panicked with my wife and children I would have trampled the corn and told them to follow me. Looking at the aerial view above, it looks like they would have eventually hit a dirt road and been able to then walk around the corn field to "safety." The corn ends no matter which direction you go.

In any case, what a great metaphor for life...feeling trapped and panicked when all you have to do is ignore the imaginary walls someone else has led you to believe are there but which you can easily trample and create your own pathway.

I understand there were plenty of maps installed in the maze too, so the family were not goo map readers either. Your point is well taken. Regardless of whether they had the technology to find their way out, they at least could have known to bust out. Although, not being map readers they may not have known that the corn field ended, From inside they wouldn't have the 1000' looking down perspective so I can understand if they feared it because they might have thought they were moving away from the exit into a deep ocean of corn! I never knew families like that existed, but I guess they do.

I love your hair! Thank you so much for injecting some reality and common sense into the situation :)

Hmm... How high are the walls of the maze? Could the family have climbed the wall and head straight in one direction? That was the way we were taught to get out when we get lost navigating in the jungle. Also I am just wondering what happened to the people who are running the place.

Back to the importance of higher maths for people. I agree Bogusia that without this we will not have the high tech gears we have today. Life would not have been better. But if you look at it, these high end maths stuff and any other subjects end up being the niches of a few select. Application wise, many people in the world still do not need these skills. Rather there are other skills that must be mastered by different people. This combination will be more beneficial to all.

The walls were made of corn, which are tall single stalks with a bunch of leaves coming off. You can't climb corn, but you can just push it aside with your hand. For sure they could have walked through the corn, if they knew which direction to go. Plus, I heard that more people take a larger step with one leg than another so it is hard to go in a straight direction without a reference. The people who run the place got a lot of free publicity. I'm sure their customers increased by many times after than news broke.

I do agree with you that it is more efficient to master a few skills than many. Specialization is often better for society. We want an expert plumber, a different expert electrician, an expert computer person, an expert cook, etc. Also, you're totally right about being able to survive and thrive without the skills that are taught in school. Many people don't even really need to be able to read. In fact, many societies get on fine still with only some portion of the population getting any kind of school at all. The rest just learn the skills they need.

We were "lost" in a corn maze once. Three toddlers, one crying baby, one VERY HOT September day. We finally found an outer wall, pushed the corn aside, snipped the fencing around the outside (ooops), and escaped. I'd planned never to do another corn maze with small children again... but now that I know the "trick" to getting through it, I may reconsider!

I've never done a corn maze before. Are they actually fun? Doesn't it cost like $10 per person or something just to walk around in corn? They never looked very good. Now caves I've been in. I do have a bit of fear getting lost in a cave without light. In the tourist caves there are paths so I'm confident I could feel my way out, but a natural cave would be terrifying before too long. No light. No possibility to push out. No way to use the rules because who knows where some of the paths lead. Thanks for the comment!

Going just left (or right) will often work. But sometimes mazes can be more complex than just a simple smushed string. Islands, bridges, etc. So another strategy you could use (assuming other people are still around in the maze):

Fear the Known - When choosing which way to go, if you see people walking toward you, assume they are coming from a dead end. Go the other way.

Statistically speaking, this should speed up your escape (more so than just wandering aimlessly). Don't believe me? Check out this simulator to test it out

That's an interesting strategy. I ran your simulator, and the first time "Fear the Unkonwn" roughly matched the random choice beating the "left turn", but the second time "Fear the Unknown" came in last at 189 moves compared to 41 and 107.

If you go the other way from people walking towards you then you go WITH them, however you've taken the shortcut of not trying the path that they just went down. Sounds like it makes sense overall in the mazes you simulate, since the mazes are funnels from the entrance to the exit -- statistically you have people entering in one corner and exiting another so they "flow" generally towards the exit. Following people will probably get you there. An equivalent strategy could also be to ID someone at a junction and let them go down a path, wait a certain amount of time to see if they come back. If they don't, then take their path because they probably got somewhere (or got trapped in a loop :( )

The two problems with the mazes in the simulation compared to Connors mazes are:

1) The Connors maze looks like it has a shared entry/exit point, so there will be no statistical flow. Equal numbers of people flow into the maze and out of the maze from the same point. As you got to the exit you would be repelled by the people entering it.

2) The family was lost at closing time I believe. I don't think they would have panicked if there were many confident people around them.

I love to think about these kinds of problems. You have a cool heuristic. Not guaranteed to find a solution, especially in a maze where EVERYONE was lost, but those don't happen in real life.

If you can join up with others then solving mazes becomes a lot easier. You can delegate people to try different paths then report back or mark the paths as I described instead of everyone walking down each path. The maze would be solved very quickly, like spreading water out. It's a form of "breadth-first search". You would likely find the shortest possible solution that way.

You're spot on that the strategy depends on some details of the maze. With separate entrances and exits, there will, as you say, be a flow. Standing in one intersection waiting... you'll count extra people 'arriving' from a direction facing the entrance and extra people 'leaving' in the direction of the exit. Even when those people are totally and completely lost, too. (Assuming once they hit the exit, they don't just turn around and keep going, to foil your plan)

As a strategy, though, it is statistical, so you win some, you lose some. With the simulation, you can do a vast number of trials to get it to settle down to an average. Depending on the maze, different strategies come out the winner.

And indeed, this is no good if there aren't people around. Just a curiousity for a fun day in a crowded maze.

I don't mean to poke fun at the lost-in-the-corn-maze family but your post was really good - esp. the diagrams. (-: And of course I had a giggle at their expense.

The thing is - I do not go into these corn mazes for just that very reason: I have a fear of getting lost in them. And as for your higher math calculations - bully for all the mathematicians out there who won't be lost in corn mazes, I'm not one of 'em. I'm a writer. They probably wouldn't find me til the next Winter freeze melted. Nope. Not going in. (-: